Systems and methods of performing NMR spectroscopy and MRI

ABSTRACT

A method of performing Nuclear Magnetic Resonance (NMR) spectroscopy or Magnetic Resonance Imaging (MRI). The methods may include: a) generating a compound comprising a first nuclear species (I 1 ), a second nuclear species (I 2 ), a third nuclear species (S), a heteronuclear coupling asymmetry (|J 1S −J 2S |) and a nuclear singlet state spin order localized on I 1  and I 2 ; b) transferring the nuclear singlet state spin order into heteronuclear magnetization localized on S by applying a single, non-recursive pulse sequence at a low magnetic field in the strong coupling regime of protons; and c) performing NMR spectroscopy or MRI with the compound comprising heteronuclear magnetization localized on S. The |J 1S −J 2S | may be non-zero. The pulse sequence may include a plurality of sequential radio frequency pulses separated by independent evolution interval. The pulse sequence may be capable of transferring at least about 75% of the nuclear singlet state spin order into heteronuclear magnetization localized on S at any |J 1S −J 2S | when the independent evolution intervals are optimized.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application claims priority to U.S. Provisional PatentApplication No. 61/717,518 filed Oct. 23, 2012, the content of which isincorporated herein by reference in its entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support from ICMIC 5P50CA128323-03. The United States federal government has certain rights inthis invention.

REFERENCE TO A COMPUTER PROGRAM LISTING APPENDIX

A computer program listing appendix is included with this applicationand the entire contents of the computer program listing appendix isincorporated herein by reference. The appendix includes duplicatecompact discs each containing a single file entitled“function_tau-_hs4.txt”, which was created on Oct. 22, 2013 and is12,213 bytes in size.

BACKGROUND

Hyperpolarization of nuclear spin ensembles has increased NMRsensitivity to a level that is now enabling detection of metabolism inbiological tissue on a time-scale of seconds. See, Ardenkjaer-Larsen, J.H.; Fridlund, B.; Gram, A.; Hansson, G.; Hansson, L.; Lerche, M. H.;Servin, R.; Thaning, M.; Golman, K. Proceedings of the National Academyof Sciences of the United States of America 2003, 100, 10158-10163; andGolman, K.; Zandt, R. I.; Lerche, M.; Pehrson, R.; Ardenkjaer-Larsen, J.H. Cancer Res 2006, 66, 10855-60, each of which is incorporated hereinin its entirety by reference. The most developed of these technologies,dynamic nuclear polarization (“DNP”, see, Carver, T. R.; Slichter, C. P.Physical Review 1953, 92, 212; Carver, T. R.; Slichter, C. P. PhysicalReview 1956, 102, 975; and Overhauser, A. W. Physical Review 1953, 92,411, each of which is incorporated herein in its entirety byreference.), in particular has already been used to detect, grade, andmonitor response to therapy in tumors. See, Albers, M. J.; Bok, R.;Chen, A. P.; Cunningham, C. H.; Zierhut, M. L.; Zhang, V. Y.; Kohler, S.J.; Tropp, J.; Hurd, R. E.; Yen, Y. F.; Nelson, S. J.; Vigneron, D. B.;Kurhanewicz, J. Cancer Res 2008, 68, 8607-15; Day, S. E.; Kettunen, M.I.; Gallagher, F. A.; Hu, D. E.; Lerche, M.; Wolber, J.; Golman, K.;Ardenkjaer-Larsen, J. H.; Brindle, K. M. Nat Med 2007, 13, 1382-7; andGolman, K.; Petersson, J. S. Acad Radiol 2006, 13, 932-42, each of whichis incorporated herein in its entirety by reference. These encouragingdevelopments have demonstrated the overall viability of NMR basedhyperpolarized methods for the study of in vivo metabolism, and arespurring development in alternative methods of hyperpolarization, suchas parahydrogen induced polarization (PHIP). See, Adams, R. W.; Aguilar,J. A.; Atkinson, K. D.; Cowley, M. J.; Elliott, P. I.; Duckett, S. B.;Green, G. G.; Khazal, I. G.; Lopez-Serrano, J.; Williamson, D. C.Science 2009, 323, 1708-11; and Bowers, C. R.; Weitekamp, D. P. Phys RevLett 1986, 57, 2645-2648, each of which is incorporated herein in itsentirety by reference. Polarization yields from the less mature PHIPtechnology are similar to DNP, and are achieved at significantly reducedinstrumental complexity and expense.

Efficient methods for transforming parahydrogen spin order intoheteronuclear magnetization at low field in arbitrary spin systems arenecessary in particular, for translating emerging contrast agents tobiomedical applications. Whereas in DNP polarization is obtaineddirectly on heteronuclei with long lifetimes (at cryogenic temperature),hyperpolarization from PASADENA is captured (at room temperature) in theform of nascent parahydrogen singlet-states, formed upon molecularaddition of parahydrogen to an unsaturated carbon-carbon bond. Theevolution of this initial ordered ensemble customarily depends on therelative strength of the static magnetic field with respect to theinternal scalar couplings. At zero field where chemical shiftdifferences vanish, the combined influence of short and long rangescalar couplings lead to a time-dependent dispersion of parahydrogenspin order across the molecule, and therefore an inevitable loss ofpolarization for any single component of spin active isotopes (e.g.¹³C). See, Theis, T.; Ledbetter, M. P.; Kervern, G.; Blanchard, J. W.;Ganssle, P. J.; Butler, M. C.; Shin, H. D.; Budker, D.; Pines, A.Journal of the American Chemical Society 2012, 134, 3987-3990, which isincorporated herein in its entirety by reference. This is an advantagefor the emerging applications of high resolution studies at zero field,but is less well suited to in vivo studies because polarization on anysingle channel of spin-active isotope (e.g. ¹³C) is exchanged fordetailed information regarding long range scalar couplings, which areunnecessary to reconstruct conversion rates across at most two reactionpathways. At high field, the truncation of transverse components in theinitial parahydrogen density matrix decreases nominal efficiency by 50%.See, Bowers, C. R.; Weitekamp, D. P. Physical Review Letters 1986, 57,2645-2648, which is incorporated herein in its entirety by reference.The intermediate strong coupling regime appears to offer a favorablemiddle ground for PHIP between high and zero fields, where the densityoperator is retained without truncation and where resonant fields can beused to selectively manipulate spin evolution.

Determining the timing, frequency, and magnitude of these applied fieldsto efficiently transform parahydrogen spin order into heteronuclearmagnetization in the strong coupling regime of protons is nontrivialthough, and earlier sequences for application to this field regime havebeen either been geared towards specific coupling patterns, or haverequired piecewise or recursive application for optimal results. See,Goldman, M.; Johannesson, H.; Axelsson, O.; Karlsson, M. Magn ResonImaging 2005, 23, 153-7; and Kadlecek, S.; Emami, K.; Ishii, M.; Rizi,R. J Magn Reson 2011, 205, 9-13, each of which is incorporated herein inits entirety by reference.

Accordingly, a need exists for a single, non-recursive pulse sequencefor transferring nuclear singlet state spin order into heteronuclearmagnetization localized on a heteronucleus at low magnetic field in thestrong coupling regime of protons.

In terms of existing theory, pulsed methods for efficiently convertingparahydrogen spin order into net heteronuclear magnetization at lowmagnetic fields are limited to systems that have only three NMR activenuclei. See, Goldman, M.; Johannesson, H.; Axelsson, O.; Karlsson, M.Magn Reson Imaging 2005, 23, 153-7; and Kadlecek, S.; Emami, K.; Ishii,M.; Rizi, R. J Magn Reson 2011, 205, 9-13, each of which is incorporatedherein in its entirety by reference. While raw singlet-states can belong lived and useful in some applications without further manipulation,when applied to biomedicine it is useful to convert these states intonet magnetization on a long-lived heteronucleus for storage and to allowsubsequent detection using standard imaging techniques. Transformingthese states into longitudinal heteronuclear magnetization alsomaximizes spectral dispersion during subsequent imaging experiments andreduces interference from the intense proton background arising fromwater in vivo. Furthermore, the initial singlet-state of an AA′XY spinsystem will generally evolve unless J_(1X)−J_(1Y)−J_(2X)+J_(2Y)=0 andJ_(1X)+J_(1Y)−J_(2X)−J_(2Y)=0. Locking magnetization on a heteronucleustherefore makes it unnecessary to synchronize detection with accruedevolution of the initial singlet-state.

Accordingly, a need exists for a single, non-recursive pulse sequencefor transferring nuclear singlet state spin order into heteronuclearmagnetization localized on a heteronucleus for a system having at leastfour NMR active nuclei.

SUMMARY

This disclosure provides methods of performing Nuclear MagneticResonance (NMR) spectroscopy or Magnetic Resonance Imaging (MRI). Themethods may include: a) generating a compound comprising a first nuclearspecies (I₁), a second nuclear species (I₂), a third nuclear species(S), a heteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) and a nuclearsinglet state spin order localized on I₁ and I₂; b) transferring thenuclear singlet state spin order into heteronuclear magnetizationlocalized on S by applying a single, non-recursive pulse sequence at alow magnetic field in the strong coupling regime of protons; and c)performing NMR spectroscopy or MRI with the compound comprisingheteronuclear magnetization localized on S. The |J_(1S)−J_(2S)| may benon-zero. The pulse sequence may include a plurality of sequential radiofrequency pulses separated by independent evolution interval. The pulsesequence may be capable of transferring at least about 75% of thenuclear singlet state spin order into heteronuclear magnetizationlocalized on S at any |_(1S)−J_(2S)| when the independent evolutionintervals are optimized.

This disclosure also provides methods including: a) generating acompound comprising a first nuclear species (I₁), a second nuclearspecies (I₂), a third nuclear species (S), a fourth nuclear species (R)and a nuclear singlet state spin order localized on I₁ and I₂; b)transferring the nuclear singlet state spin order into heteronuclearmagnetization localized on S by applying a pulse sequence at a lowmagnetic field in the strong coupling regime of protons; and c)performing NMR spectroscopy or MRI with the compound comprisingheteronuclear magnetization localized on S.

This disclosure also provides methods including: a) determiningJ-couplings for a compound comprising a first nuclear species (I₁), asecond nuclear species (I₂), a third nuclear species (S), aheteronuclear coupling asymmetry (|J_(1S-)J_(2S)|) and a nuclear singletstate spin order localized on I₁ and I₂; b) calculating optimalevolution intervals for a single, non-recursive pulse sequence at lowmagnetic field in the strong coupling regime of protons using theJ-couplings, the pulse sequence comprising a sequential plurality ofradio frequency pulses separated by independent evolution intervals; c)generating the compound; d) transferring the nuclear singlet state spinorder into heteronuclear magnetization localized on S by applying thepulse sequence with optimal evolution intervals to the compound; and e)performing NMR spectroscopy or MRI with the compound comprisingheteronuclear magnetization localized on S. The pulse sequence maytransfer at least about 75% of the nuclear singlet state spin order intoheteronuclear magnetization localized on S at any |J_(1S)−J_(2S)|.

This disclosure also provides NMR spectroscopy and MRI systemsconfigured to perform the methods described herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart illustrating methods of performing NuclearMagnetic Resonance spectroscopy or Magnetic Resonance Imaging (MRI) inaccordance with an embodiment of this disclosure.

FIG. 2 is a schematic representation of the evolution of density matrixcomponents (top) corresponding to a hyper-SHIELDED pulse sequence(bottom).

FIG. 3 is a graph of the polarization yield as a function of homonuclearproton coupling (J₁₂) for hyper-SHIELDED.

FIG. 4 is a graph of theoretical maximized polarization transferefficiency versus heteronuclear coupling asymmetry comparing thehyper-SHIELDED pulse sequence (solid) to a non-recursive implementationof the GPS comparison sequence of Example 2.

FIG. 5 is a Boltzmann polarized carbon-13 spectrum acquired from anaqueous solution containing 170 millimoles of the reaction product2-hydroxy, 1-¹³C-ethylpropionate-d₃ (HEP).

FIG. 6 is a reaction schematic for synthesizing parahydrogenated2-hydroxy, 1-¹³C-ethylpropionate-d₃ (HEP).

FIG. 7 are experimentally determined yields for the hyper-SHIELDED pulsesequence (left) and the GPS comparison sequence (right) of Example 2.

FIG. 8 is a schematic representation of the evolution of density matrixcomponents (top) corresponding to a hyper-SHIELDED-4 pulse sequence(bottom).

DETAILED DESCRIPTION

The methods and systems disclosed herein are not limited in theirapplications to the details of construction and the arrangement ofcomponents described herein. The methods and apparatuses are capable ofother embodiments and of being practiced or of being carried out invarious ways. Also it is to be understood that the phraseology andterminology used herein is for the purpose of description only, andshould not be regarded as limiting. Ordinal indicators, such as first,second, and third, as used in the description and the claims to refer tovarious structures, are not meant to be construed to indicate anyspecific structures, or any particular order or configuration to suchstructures. All methods described herein can be performed in anysuitable order unless otherwise indicated herein or otherwise clearlycontradicted by context. The use of any and all examples, or exemplarylanguage (e.g., “such as”) provided herein, is intended merely to betterilluminate the methods and apparatuses disclosed herein and does notpose a limitation on the scope of the methods and apparatuses unlessotherwise claimed. No language in the specification, and no structuresshown in the drawings, should be construed as indicating that anynon-claimed element is essential to the practice of the methods andapparatuses disclosed herein.

Recitation of ranges of values herein are merely intended to serve as ashorthand method of referring individually to each separate valuefalling within the range, unless otherwise indicated herein, and eachseparate value is incorporated into the specification as if it wereindividually recited herein. For example, if a concentration, volume orthe like range is stated as 1% to 50%, it is intended that values suchas 2% to 40%, 10% to 30%, or 1% to 3%, etc., are expressly enumerated inthis specification. These are only examples of what is specificallyintended, and all possible combinations of numerical values between andincluding the lowest value and the highest value enumerated are to beconsidered to be expressly stated in this application.

Further, no admission is made that any reference, including anynon-patent or patent document cited in this specification, constitutesprior art. In particular, it will be understood that, unless otherwisestated, reference to any document herein does not constitute anadmission that any of these documents forms part of the common generalknowledge in the art in the United States or in any other country. Anydiscussion of the references states what their authors assert, and theapplicant reserves the right to challenge the accuracy and pertinence ofany of the documents cited herein.

This disclosure provides methods of performing Nuclear MagneticResonance (NMR) spectroscopy or Magnetic Resonance Imaging (MRI). Thisdisclosure also provides systems configured to execute the methods ofperforming NMR spectroscopy or MRI.

I. Methods

Referring to FIG. 1, this disclosure provides a method of performing NMRspectroscopy or MRI spectroscopy. The method may comprise: a) generatinga compound comprising a first nuclear species (I₁), a second nuclearspecies (I₂), a third nuclear species (S) and a nuclear singlet statespin order localized on I₁ and I₂ 20; b) transferring the nuclearsinglet state spin order into heteronuclear magnetization localized on Sby applying a single, non-recursive pulse sequence at a low magneticfield in the strong coupling regime of protons 30; and c) performing NMRspectroscopy or MRI with the compound comprising heteronuclearmagnetization localized on S 40.

The compound may comprise a heteronuclear coupling asymmetry(|J_(1S)−J_(2S)|). In certain embodiments, |J_(1S)−J_(2S)| may benon-zero.

A. Generating a Compound Comprising a Nuclear Singlet State Spin Order

The method may comprise generating a compound comprising a first nuclearspecies (I₁), a second nuclear species (I₂), a third nuclear species(S), a heteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) and a nuclearsinglet state spin order localized on I₁ and I₂. The method may comprisegenerating a compound comprising a first nuclear species (I₁), a secondnuclear species (I₂), a third nuclear species (S), a fourth nuclearspecies (R) and a nuclear singlet state spin order localized on I₁ andI₂.

Generating a compound comprising a first nuclear species (I₁), a secondnuclear species (I₂), a third nuclear species (S), a heteronuclearcoupling asymmetry (|J_(1S)−J_(2S)|) and a nuclear singlet state spinorder localized on I₁ and I₂ may be executed by any known method ofcreating a nuclear singlet state spin order. Generating a compoundcomprising a first nuclear species (I₁), a second nuclear species (I₂),a third nuclear species (S), a fourth nuclear species (R) and a nuclearsinglet state spin order localized on I₁ and I₂ may be executed by anyknown method of creating a nuclear singlet state spin order. Generatinga compound comprising a nuclear singlet state spin order may comprisehyperpolarizing the compound by parahydrogen induced polarization(PHIP), any method of forming a generic singlet state other than protonscapable of endowing its spin order onto another molecule, singlet statesformed by running the pulse sequences disclosed herein in reverse, andcombinations thereof. Examples of suitable methods include, but are notlimited to, those disclosed in U.S. Pat. Nos. 6,574,495 and 6,872,380,each of which is incorporated herein in its entirety by reference.

The compound may be hyperpolarized.

Nuclear species may be any NMR-active nuclei capable of exhibiting thespin order and magnetization properties described herein. Examples ofnuclear species include, but are not limited to ¹H, ¹³C, ¹⁵N, ³¹P, ¹⁹F,²⁹Si, and ¹⁰³Rh. Nuclear species may be suited to hyperpolarization.Nuclear species may be suited to parahydrogen induced polarization(PHIP).

Compounds may have naturally occurring amounts of nuclear species or maybe enriched to contain more nuclear species than naturally occurringcompounds.

The heteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) may be non-zero.Without wishing to be bound by theory, in the limit that theheteronuclear coupling asymmetry approaches zero, the overall pulsesequence duration required for optimal magnetization transfer approachesinfinity.

B. Transferring the Nuclear Singlet State Spin Order into HeteronuclearMagnetization

The method may comprise transferring the nuclear singlet state spinorder into heteronuclear magnetization localized on S by applying asingle, non-recursive pulse sequence at a low magnetic field in thestrong coupling regime of protons.

As used herein, low magnetic field includes a magnetic field that isnon-zero and less than about 100 mT.

The pulse sequences 100, 200 disclosed herein may comprise a sequentialplurality of radio frequency pulses 110, 111, 112, 113, 210, 211, 212,213, 214, 215 separated by independent evolution intervals 120, 121,122, 123, 220, 221, 222, 223, 224, 225. The pulse sequences may compriseat least 4 sequential radio frequency pulses or at least 6 sequentialradio frequency pulses. The pulse sequences may comprise 4, 6, 8, 10,12, 14, 16, 18, 20 or more sequential radio frequency pulses. Highernumbers of radio frequency pulses provide greater numbers of independentevolution intervals, thereby allowing higher order spin systems to beoptimized.

The pulse sequence may comprise a first portion 130, 230 and a secondportion 131, 231. The first portion may convert the nuclear singletstate spin order localized on I₁ and I₂ into a pure state which iscoupled to S. The second portion may convert the pure state which iscoupled to S into longitudinal net magnetization on S. The first andsecond portion may contain equal or unequal numbers of radio frequencypulses or evolution intervals.

The duration of the pulse sequence may equal the sum of the independentevolution intervals.

The pulse sequences may further comprise applying focusing pulsesbetween the sequential radio frequency pulses. A non-limiting example ofapplying focusing pulses between the sequential radio frequency pulsesincludes applying focusing pulses at ¾ and ¾ of each independentevolution interval.

The pulse sequences disclosed herein is configured to transfer at leastabout 75%, at least about 80%, at least about 85%, at least about 90%,at least about 95%, at least about 96%, at least about 97%, at leastabout 98%, at least about 99% or about 100% of the nuclear singlet statespin order into heteronuclear magnetization localized on S at any|J_(1S)−J_(2S)| when the independent evolution intervals are optimized.

The pulse sequences may be optimized in accordance with techniques knownto those skilled in the relevant art. The pulse sequences may beoptimized with techniques described herein. The pulse sequences may beoptimized by calculating optimal evolution intervals as describedherein. It should be recognized that pulse sequence optimizationtypically proceeds without adding, removing, reordering or altering theradio frequency pulses.

Referring to FIG. 2, the pulse sequences 100 disclosed herein maycomprise the following sequential elements: a) a time t₁ aftergenerating the compound 120; b) a 180(+x) pulse on I₁ and I₂ 110; c) atime t₂ 121; d) a 90(+y) pulse on S 111; e) a time t₃ 122; f) a 180(+x)pulse on I₁ and I₂ 112; g) a time t₄ 123; and h) a 90(+x) pulse on S113. Referring to FIG. 2, the pulse sequences 100 disclosed herein maycomprise the following sequential steps: a) waiting a time t₁ aftergenerating the compound 120; b) applying a 180(+x) pulse on I₁ and I₂110; c) waiting a time t₂ 121; d) applying a 90(+y) pulse on S 111; e)waiting a time t₃ 122; f) applying a 180(+x) pulse on I₁ and I₂ 112; g)waiting a time t₄ 123; and h) applying a 90(+x) pulse on S 113. Incertain embodiments, t₁, t₂, t₃ and t₄ may be selected to maximizetransfer of the nuclear singlet state spin order localized on I₁ and I₂into longitudinal net magnetization on S. In certain embodiments, t₁ andt₂ may be selected to maximize transfer of the nuclear singlet statespin order localized on I₁ and I₂ into a pure state which is coupled toS, t₃ and t₄ may be selected to maximize transfer of the pure statewhich is coupled to S into longitudinal net magnetization on S, or acombination thereof. Referring to FIG. 2, the pulse sequence 100 maycomprise a first portion 130 and second portion 131. The first portionmay include steps a)-d). The second portion may include steps e)-h).

Referring to FIG. 8, the pulse sequences 200 disclosed herein maycomprise the following sequential elements: a) a time t₁ aftergenerating the compound 220; b) a 180(+x) pulse on S 210; c) a time t₂221; d) a 180(+x) pulse on I₂ and I₂ 211; e) a time t₃ 222; f) a 90(+y)pulse on S 212; g) a time t₄ 223; h) a 180(+x) pulse on S 213; i) a timet₅ 224; j) a 180(+x) pulse on I₁ and I₂ 214; k) a time t₆ 225; and 1) a90(+x) pulse on S 215. Referring to FIG. 8, the pulse sequences 200disclosed herein may comprise the following sequential steps: a) waitinga time t₁ after generating the compound 220; b) applying a 180(+x) pulseon S 210; c) waiting a time t₂ 221; d) applying a 180(+x) pulse on I₁and I₂ 211; e) waiting a time t₃ 222; f) applying a 90(+y) pulse on S212; g) waiting a time t₄ 223; h) applying a 180(+x) pulse on S 213; i)waiting a time t₅ 224; j) applying a 180(+x) pulse on I₁ and I₂ 214; k)waiting a time t₆ 225; and 1) applying a 90(+x) pulse on S 215. Incertain embodiments, t₁, t₂, t₃, t₄, t₅ and t₆ may be selected tomaximize transfer of the nuclear singlet state spin order localized onI₁ and I₂ into longitudinal net magnetization on S. In certainembodiments, t₁, t₂ and t₃ may be selected to maximize transfer of thenuclear singlet state spin order localized on and I₂ into a pure statewhich is coupled to S, t₄, t₅ and t₆ may be selected to maximizetransfer of the pure state which is coupled to S into longitudinal netmagnetization on S, or a combination thereof. Referring to FIG. 8, thepulse sequence 200 may comprise a first portion 230 and second portion231. The first portion may include steps a)-f). The second portion mayinclude steps g)-l).

The pulse sequence may be preceded by a decoupling sequence. Thedecoupling sequence may be a sequence for decoupling I₁ and I₂, a protondecoupling sequence, or a combination thereof.

1. Hyper-SHIELDED Pulse Sequence

In some embodiments, the pulse sequence may comprise a hyper-SHIELDEDpulse sequence. The theory behind the hyper-SHIELDED pulse sequence fora three spin system is as follows.

The Hamiltonian of the three spin system (AA′X=I₁I₂S) formed from theparahydrogen addition product (PASADENA, see, Bowers, C. R.; Weitekamp,D. P. Physical Review Letters 1986, 57, 2645-2648; and Bowers, C. R.;Weitekamp, D. P. Journal of the American Chemical Society 1987, 109,5541-5542, each of which is incorporated herein in its entirety byreference) and a coupled heteronucleus in the strong proton couplingregime can be written as:H=2π[J ₁₂(I ₁ ·I ₂)+J _(1S) I _(1z) S _(z) +J _(2S) I _(2z) S_(z)].  (1)

The initial density matrix of parahydrogen at low field in the strongcoupling regime of protons can be written:σ₀=¼−I ₁ ·I ₂.  (2)

The I_(1z)I_(2z) component of this initial density matrix commutes withall components, and hence does not evolve under the Hamiltonian inEq. 1. The remainder of the initial density matrix in the PASADENAaddition product evolves during the interval t₁ under the influence ofthe Hamiltonian according to the following expression:

$\begin{matrix}{\sigma_{1}\overset{t_{1}}{\rightarrow}{\left\lbrack {{\sin^{2}\theta} + {\left( {\cos^{2}\theta} \right){\cos\left( {2{\pi\Omega}\; t\; 1} \right)}}} \right\rbrack\left( {{I_{1x}I_{2x}} + {I_{1y}I_{2y}}} \right)}} & \left( {3a} \right) \\{{+ \left( {\cos\;\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{1}} \right)}2\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)S_{z}} & \left( {3b} \right) \\{{{+ \left( {\sin\;\theta} \right)}{\left( {\cos\;\theta} \right)\left\lbrack {1 - {\cos\left( {2{\pi\Omega t}_{1}} \right)}} \right\rbrack}\left( {I_{1z} - I_{2z}} \right)S_{z}}{where}{{{\cos\;\theta} = \frac{\Delta}{\sqrt{1 + \Delta^{2}}}},{{\sin\;\theta} = \frac{\Delta}{\sqrt{1 + \Delta^{2}}}},{\Delta = {\left\lbrack {J_{1s} - J_{2s}} \right\rbrack\left( {2 \cdot J_{12}} \right)^{- 1}}},{and}}{\Omega = {{J_{12}\left( {1 + \Delta^{2}} \right)}^{\frac{1}{2}}.}}} & \left( {3c} \right)\end{matrix}$

After applying a 180(+x) pulse on protons, the density operator σ₂evolves according to:

$\begin{matrix}{\left. {\sigma_{2}\overset{t_{2}}{\rightarrow}{\left\lbrack {{{- \cos}\; 2\;{\theta\left( {\sin^{2}\theta} \right)}} + {\frac{1}{2}\sin^{2}2{\theta\left( {{\cos\left( {2{\pi\Omega}\; t_{1}} \right)} + {\cos\left( {2{\pi\Omega}\; t_{2}} \right)}} \right)}} + {\cos\; 2\;{\theta\left( {\cos^{2}\theta} \right)}{\cos\left( {2{\pi\Omega}\; t_{1}} \right)}{\cos\left( {2{\pi\Omega}\; t_{2}} \right)}}} \right\rbrack + {\left( {\cos^{2}\theta} \right){\sin\left( {2{\pi\Omega}\; t_{1}} \right)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}}}} \right\rbrack\left( {{I_{1x}I_{2x}} + {I_{1y}I_{2y}}} \right)} & \left( {4a} \right) \\{{+ \left\lbrack {{{\sin\left( {2\theta} \right)}{\sin(\theta)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}} + {{\cos\left( {2\theta} \right)}{\cos(\theta)}\left( {2{\pi\Omega}\; t_{1}} \right){\sin\left( {2{\pi\Omega}\; t_{2}} \right)}} - {{\cos(\theta)}{\sin\left( {2{\pi\Omega}\; t_{1}} \right)}{\cos\left( {2{\pi\Omega}\; t_{2}} \right)}}} \right\rbrack}2\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)S_{z}} & \left( {4b} \right) \\{{+ \left\lbrack {{- \frac{1}{2}}{\sin\left( {2\theta} \right)}\left( {{\cos\left( {2\theta} \right)} + {2{\sin^{2}(\theta)}} - {2{\cos^{2}(\theta)}{\cos\left( {2{\pi\Omega}\; t_{1}} \right)}} + {{\cos\left( {2\theta} \right)}{\cos\left( {2{\pi\Omega}\; t_{1}} \right)}{\cos\left( {2{\pi\Omega}\; t_{2}} \right)}} + {{\sin\left( {2{\pi\Omega}\; t_{1}} \right)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}}} \right)} \right\rbrack}\left( {I_{1z} - I_{2z}} \right)S_{z}} & \left( {4c} \right)\end{matrix}$

In order to drive the terms in Eq. 4 exclusively to Eq. 4c, theintervals t₁ and t₂ are chosen to satisfy Equations 5a and 5b:

$\begin{matrix}{{{{{- \cos}\; 2{\theta sin}^{2}\theta} + {\frac{1}{2}\sin^{2}2{\theta\left( {{\cos\left( {2\pi\;{\Omega t}_{1}} \right)} + {\cos\left( {2{\pi\Omega}\; t_{2}} \right)}} \right)}} + {{\cos\left( {2\theta} \right)}\cos^{2}{{\theta cos}\left( {2{\pi\Omega}\; t_{1}} \right)}{\cos\left( {2{\pi\Omega}\; t_{2}} \right)}} + {\cos^{2}{{\theta sin}\left( {2{\pi\Omega}\; t_{1}} \right)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}}} = 0},} & \left( {5a} \right) \\{{{{\sin\left( {2\theta} \right)}{\sin(\theta)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}} + {{\cos\left( {2\theta} \right)}{\cos(\theta)}{\cos\left( {2{\pi\Omega}\; t_{1}} \right)}{\sin\left( {2{\pi\Omega}\; t_{2}} \right)}} - {{\cos(\theta)}{\sin\left( {2{\pi\Omega}\; t_{1}} \right)}{\cos\left( {2{\pi\Omega}\; t_{2}} \right)}}} = 0} & \left( {5b} \right)\end{matrix}$

A 90(+y) pulse on the S spin then converts the state(I_(1z)−I_(2x))S_(z) into (I_(1z)−I_(2z))S_(x). During the subsequentinterval t₃, this state evolves into three terms:

$\begin{matrix}{\sigma_{3} = {{\left( {I_{1z} - I_{2z}} \right)S_{x}}\overset{t_{3}}{\rightarrow}{{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}\left( {I_{1z} - I_{2z}} \right)S_{x}}}} & \left( {6a} \right) \\{{+ {\cos(\theta)}}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}\frac{1}{2}{S_{y}\left( {I - {4I_{1z}I_{2z}}} \right)}} & \left( {6b} \right) \\{{- {\sin(\theta)}}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}2\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)S_{x}} & \left( {6c} \right)\end{matrix}$

A proton 180(+x) pulse is then applied, and during the subsequentinterval t₄, the density matrix evolves according to the expression:

$\begin{matrix}{\sigma_{4}\overset{t_{4}}{\rightarrow}{\left\lbrack {{{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}{\cos\left( {2{\pi\Omega}\; t_{4}} \right)}} + {{\cos\left( {2\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}{\sin\left( {2{\pi\Omega}\; t_{4}} \right)}}} \right\rbrack\left( {I_{1z} - I_{2z}} \right)S_{x}}} & \left( {7a} \right) \\{{+ \left\lbrack {{{\cos(\theta)}{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}{\sin\left( {2{\pi\Omega}\; t_{4}} \right)}} - {{\sin\left( {2\theta} \right)}{\sin(\theta)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}} - {{\cos(\theta)}{\cos\left( {2\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}{\cos\left( {2{\pi\Omega}\; t_{4}} \right)}}} \right\rbrack}\frac{1}{2}{S_{y}\left( {I - {4I_{1z}I_{2z}}} \right)}} & \left( {7b} \right) \\{{+ \left\lbrack {{{\sin(\theta)}{\cos\left( {2\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}{\cos\left( {2{\pi\Omega}\; t_{4}} \right)}} - {{\sin(\theta)}{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}{\sin\left( {2{\pi\Omega}\; t_{4}} \right)}} - {{\sin\left( {2\theta} \right)}{\cos(\theta)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}}} \right\rbrack}2\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)S_{x}} & \left( {7c} \right)\end{matrix}$

The intervals t₃ and t₄ are chosen to satisfy the following set ofequations:

$\begin{matrix}{\mspace{79mu}{{{{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}{\cos\left( {2{\pi\Omega}\; t_{4}} \right)}} + {{\cos\left( {2\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}{\sin\left( {2{\pi\Omega}\; t_{4}} \right)}}} = 0}} & \left( {8a} \right) \\{{{{\sin(\theta)}{\cos\left( {2\theta} \right)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}{\cos\left( {2{\pi\Omega}\; t_{4}} \right)}} - {{\sin(\theta)}{\cos\left( {2{\pi\Omega}\; t_{3}} \right)}{\sin\left( {2{\pi\Omega}\; t_{4}} \right)}} - {{\sin\left( {2\theta} \right)}{\cos(\theta)}{\sin\left( {2{\pi\Omega}\; t_{3}} \right)}}} = 0} & \left( {8b} \right)\end{matrix}$

This condition is satisfied when:tan(2πΩt ₃)=−1/√{square root over (1+2 cos(2θ))}  (9a)tan(2πΩt ₄)=1/√{square root over (1+2 cos(3θ))}  (9b)

Finally, a 90(+x) pulse converts the term from Eq. 7b into longitudinalmagnetization on the heteronucleus for storage until subsequentdetection in vivo. The pulse sequence diagram (bottom) and schematic ofspin evolution represented by equations 2-7 (top) is illustrated in FIG.2. The numbers in the schematic of spin evolution correspond to equationnumbers for the density matrices set forth above.

2. Hyper-SHIELDED-4 Pulse Sequence

In some embodiments, the pulse sequence may comprise a hyper-SHIELDED-4(hS4) pulse sequence. The theory behind the hyper-SHIELDED-4 pulsesequence for a four spin system is as follows.

The Hamiltonian of the four spin system formed by the addition ofparahydrogen to a molecule containing two heteronuclei can be writtenas:

$\begin{matrix}{H = {2{{\pi\left\lbrack {{J_{12}\left( {{I_{1x}I_{2x}} + {I_{1y}I_{2y}} + {I_{1z}I_{2z}}} \right)} + {J_{1S}I_{1z}S_{z}} + {J_{1R}I_{1z}R_{z}} + {J_{2S}I_{2z}S_{z}} + {J_{2R}I_{2z}R_{z}} + {J_{SR}S_{z}R_{z}}} \right\rbrack}.}}} & (10)\end{matrix}$

In this expression, I₁ and I₂ refer to protons while S and R refer toheteronuclei which are weakly coupled to one another and to the protons.The initial density matrix of parahydrogen can be written in the strongcoupling regime of protons as:σ₁=¼−(I _(1x) I _(2x) +I _(1y) I _(2y) +I _(1z) I _(2z))  (11)

The I_(1z)I_(2z) term component of this initial density matrix commuteswith Hamiltonian given in Equation 1. The remainder of the initialdensity matrix evolves with hyper-SHIELDED-4 (hS4, FIG. 8) during theinterval t₁ under the influence of the Hamiltonian according to thefollowing expression:

$\begin{matrix}{{\sigma_{1}\left( t_{1} \right)} = {{\frac{1}{2}\left\lbrack {{\sin^{2}\theta_{1}} + {\cos\;\theta_{1}{\cos\left( {2{\pi\Omega}_{1}t_{1}} \right)}} + {\sin^{2}\theta_{2}} + {\cos\;\theta_{2}{\cos\left( {2{\pi\Omega}_{2}t_{2}} \right)}}} \right\rbrack}\left( {{I_{1x}I_{2x}} + {I_{1y}I_{2y}}} \right)}} & \left( {12a} \right) \\{{+ {\frac{1}{2}\left\lbrack {{\sin^{2}\theta_{1}} + {\cos\;\theta_{1}{\cos\left( {2{\pi\Omega}_{1}t_{1}} \right)}} - {\sin^{2}\theta_{2}} - {\cos\;\theta_{2}{\cos\left( {2{\pi\Omega}_{2}t_{2}} \right)}}} \right\rbrack}}4\left( {{I_{1x}I_{2x}} + {I_{1y}I_{2y}}} \right)S_{z}R_{z}} & \left( {12b} \right) \\{{+ {\frac{1}{2}\left\lbrack {{\cos\;\theta_{1}{\sin\left( {2{\pi\Omega}_{1}t_{1}} \right)}} - {\cos\;\theta_{2}{\sin\left( {2{\pi\Omega}_{2}t_{2}} \right)}}} \right\rbrack}}2\left( {{I_{1y}I_{2x}} + {I_{1x}I_{2y}}} \right)S_{z}} & \left( {12c} \right) \\{{+ {\frac{1}{2}\left\lbrack {{\cos\;\theta_{1}{\sin\left( {2{\pi\Omega}_{1}t_{1}} \right)}} - {\cos\;\theta_{2}{\sin\left( {2{\pi\Omega}_{2}t_{2}} \right)}}} \right\rbrack}}2\left( {{I_{1y}I_{2x}} + {I_{1x}I_{2y}}} \right)R_{z}} & \left( {12d} \right) \\{{+ {\frac{1}{4}\left\lbrack {{\sin\; 2\;{\theta_{1}\left( {1 - {\cos\left( {2{\pi\Omega}_{1}t_{1}} \right)}} \right)}} - {\sin\; 2\;{\theta_{2}\left( {1 - {\cos\left( {2{\pi\Omega}_{2}t_{2}} \right)}} \right)}}} \right\rbrack}}\left( {I_{1z} - I_{1z}} \right)S_{z}} & \left( {12e} \right) \\{{+ {\frac{1}{4}\left\lbrack {{\sin\; 2\;{\theta_{1}\left( {1 - {\cos\left( {2{\pi\Omega}_{1}t_{1}} \right)}} \right)}} - {\sin\; 2\;{\theta_{2}\left( {1 - {\cos\left( {2{\pi\Omega}_{2}t_{2}} \right)}} \right)}}} \right\rbrack}}\left( {I_{1z} - I_{1z}} \right)R_{z}} & \left( {12f} \right) \\{where} & \; \\{\mspace{79mu}{{\Omega_{1} = {J_{12}\sqrt{1 + \Delta_{1}^{2}}}}\mspace{79mu}{\Omega_{2} = {J_{12}\sqrt{1 + \Delta_{2}^{2}}}}\mspace{79mu}{{\sin\;\theta_{1}} = \frac{1}{\sqrt{1 + \Delta_{1}^{2}}}}\mspace{79mu}{{\sin\;\theta_{2}} = \frac{1}{\sqrt{1 + \Delta_{2}^{2}}}}\mspace{79mu}{{\cos\;\theta_{1}} = \frac{\Delta}{\sqrt{1 + \Delta_{1}^{2}}}}\mspace{79mu}{{\cos\;\theta_{2}} = \frac{\Delta}{\sqrt{1 + \Delta_{2}^{2}}}}\mspace{79mu}{\Delta_{1} = \frac{J_{1S} + J_{1R} - J_{2S} - J_{2R}}{2J_{12}}}\mspace{79mu}{\Delta_{2} = \frac{J_{1S} - J_{1R} - J_{2S} + J_{2R}}{2J_{12}}}}} & (13)\end{matrix}$

The first half of hS4 (t₁, t₂, t₃) converts the initial singlet-state toa pure 12e state which is coupled to heteronucleus S. The density matrixfollowing propagation through t₁, t₂, t₃ can be written as:σ_(N)(t ₁ ,t ₂ ,t ₃)=e ^(−iHt) ³ [R _(X) ^(I)(π)]⁻¹ e ^(−iHt) ² [R _(X)^(S)(π)]⁻¹ ·e ^(−iHt) ¹ σ₀ e ^(iHt) ¹ R _(X) ^(S)(π)e ^(iHt) ² R _(X)^(I)(π)e ^(iHt) ³   (14)

Evolution delays t₁, t₂, and t₃ are then adjusted to minimize thedifference between the σ_(N) and 12e according to the followingequation:min[σ_(N)(t ₁ ,t ₂ ,t ₃)−12e]  (15)

A 90(+y) pulse on the S spin then converts the state 12e(I_(1z)−I_(2z))S_(z)) into (I_(1z)−I_(2z))S_(x). During the subsequentinterval t₄, this state then evolves into eight terms:

$\begin{matrix}{{\sigma_{N}\left( t_{4} \right)} = {{{\cos\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{{\cos\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} - {{\cos\left( {\theta_{1} - \theta_{2}} \right)}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}{S_{x}\left( {I_{1z} - I_{2z}} \right)}}} & \left( {16a} \right) \\{{- {{\sin\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\cos\;\theta_{1}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} + {\cos\;\theta_{2}{\cos\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}}{S_{x}\left( {I - {4I_{1z}I_{2z}}} \right)}R_{z}} & \left( {16b} \right) \\{{+ {{\cos\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\cos\;\theta_{1}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} + {\cos\;\theta_{2}{\cos\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}}\frac{1}{2}{S_{y}\left( {I - {4I_{1z}I_{2z}}} \right)}} & \left( {16c} \right) \\{{+ {{\cos\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\cos\;\theta_{1}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} - {{\cos\left( \;{\theta_{1} - \theta_{2}} \right)}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}}2{S_{y}\left( {I_{1z} - I_{2z}} \right)}R_{z}} & \left( {16d} \right) \\{{{- {{\cos\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\sin\left( \;{\theta_{1} - \theta_{2}} \right)}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}} \right\rbrack}} \cdot 4}{S_{y}\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)}R_{z}} & \left( {16e} \right) \\{{- {{\sin\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\sin\;\theta_{1}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} + {\sin\;\theta_{2}{\cos\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}}4{S_{y}\left( {{I_{1y}I_{2x}} - {I_{1x}I_{2y}}} \right)}R_{z}} & \left( {16f} \right) \\{{- {{\cos\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {{\sin\;\theta_{1}{\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\cos\left( {{\pi\Omega}_{2}t_{4}} \right)}} + {\sin\;\theta_{2}{\cos\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}}} \right\rbrack}}2{S_{x}\left( {{I_{1y}I_{2x}} + {I_{1x}I_{2y}}} \right)}} & \left( {16g} \right) \\{{- {{\sin\left( {\pi\; J_{SR}t_{4}} \right)}\left\lbrack {\sin\;\left( {\theta_{1} - \theta_{2}} \right){\sin\left( {{\pi\Omega}_{1}t_{4}} \right)}{\sin\left( {{\pi\Omega}_{2}t_{4}} \right)}} \right\rbrack}} \cdot {\quad{2{S_{y}\left( {{I_{1y}I_{2x}} + {I_{1x}I_{2y}}} \right)}}}} & \left( {16h} \right)\end{matrix}$

Since the I_(1z)I_(2z) term does not evolve with time, the second phaseof hS4 transforms σ_(N) into a pure single quantum S-coherence (term16c).

A 180(+x) pulse on the S channel is applied following evolution delayt₄. A 180(+x) pulse on the proton channel is then applied following thet₅ interval. The density matrix then evolves during the t₆ evolutiondelay to the targeted final state:σ_(F)(t ₄ ,t ₅ ,t ₆)=e ^(−iHt) ⁶ [R _(X) ^(I)(π)]⁻¹ e ^(−iHt) ⁵ [R _(X)^(S)(π)]⁻¹ ·e ^(−iHt) ⁴ σ_(int) e ^(iHt) ⁴ R _(X) ^(S)(π)e ^(iHt) ⁵ R_(X) ^(I)(π)e ^(iHt) ⁶   (17)

The time intervals (t₄, t₅, and t₆) are adjusted to minimize thedifference between the up and the desired pure 16c term:min[σ_(N)(t ₁ ,t ₂ ,t ₃)−16c]  (18)

Finally, a 90(+x) pulse converts the 16c term into longitudinal netmagnetization on the heteronucleus S for storage until subsequentdetection.

It should be appreciated that the phases discloses herein can beincremented sequentially by an arbitrary amount to achieve similareffect. For example, if all pulses received a phase increment ofdelta(phi), the effect of the pulse sequence would be similar.

C. Determining J-Couplings

J-couplings can be determined in accordance with techniques known tothose skilled in the relevant arts. The method may comprise determiningJ-couplings for a compound comprising a first nuclear species (I₁), asecond nuclear species (I₂), a third nuclear species (S), aheteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) and a nuclear singletstate spin order localized on I₁ and I₂.

Determining J-couplings for a compound may comprise experimentallydetermining J-couplings, theoretically calculating J-couplings andcombinations thereof. Examples of experimentally determining J-couplingsinclude, but are not limited to, measuring first order couplings at highfield, HSQC, HMQC, COSY, or multidimensional acquisitions that allowscalar evolution to be detected indirectly, and combinations thereof.Examples of theoretically calculating J-couplings include, but are notlimited to, density functional theory calculations, ab initiocalculations, and combinations thereof. Determining J-couplings for acompound may comprise calculations involving equations 1-18.

D. Calculating Optimal Evolution Intervals

Calculating optimal evolution intervals can be performed in accordancewith techniques known to those skilled in the relevant arts. The methodmay comprise calculating optimal evolution intervals for a single,non-recursive pulse sequence at low magnetic field in the strongcoupling regime of protons. The method may comprise calculating optimalevolution intervals using the J-couplings determined in the determiningJ-couplings for a compound step.

Calculating optimal evolution intervals may comprise inverting a densitymatrix expression representing the evolution of spin states of thecompound during application the pulse sequence to the compound,minimizing the difference between a density matrix expressionrepresenting the evolution of spin states of the compound duringapplication of the pulse sequence and a desired state which is coupledto S, or a combination thereof.

Calculating optimal evolution intervals may comprise use of a computercode for minimizing the difference between a density matrix expressionrepresenting the evolution of a compound during applying the pulsesequence and a desired state which is couple to S. Examples of acomputer code for this purpose include, but are not limited to, thehyper-SHIELDED minimization code and the hyper-SHIELDED-4 minimizationcode described herein. The hyper-SHIELDED minimization code is set forthbelow. The hyper-SHIELDED-4 minimization code is set forth in thecomputer program listing appendix in a file entitled file entitled“function_tau-_hs4.txt”.

E. Performing NMR Spectroscopy or MRI

Performing NMR spectroscopy or MRI can be executed in accordance withtechniques known to those skilled in the relevant arts. Examples ofperforming NMR spectroscopy or MRI include, but are not limited to,collecting, processing, storing and/or displaying NMR spectroscopy datain accordance with techniques known to those skilled in the relevantarts, infusing the compound in vivo for MRI in accordance withtechniques known to those skilled in the relevant arts, and combinationsthereof.

II. Systems

This disclosure provides NMR spectroscopy or MRI systems configured toexecute the methods disclosed herein. Suitable NMR spectroscopy or MRIsystems are known to those skilled in the relevant arts and capable ofbeing configured to execute the methods disclosed herein. NMRspectroscopy or MRI systems may be configured to deliver the pulsesequences disclosed herein. For example, NMR spectroscopy or MRI systemsmay be pre-configured using software to deliver the pulse sequencesdisclosed herein.

EXAMPLES

The following examples are presented to illustrate the present inventionand to assist one of ordinary skill in making and using the same. Theexamples are not intended in any way to otherwise limit the scope of theinvention.

Example 1 Hyper-SHIELDED Pulse Sequence

Approximately 98% parahydrogen gas was synthesized by pulsing ambientresearch grade hydrogen gas at 14 bar (200 psi) into a catalyst-filled(iron oxide) copper chamber held at 14 K using a previously describedsemi-automated parahydrogen generator. See, Feng, B. B.; Coffey, A. M.;Colon, R. D.; Chekmenev, E. Y.; Waddell, K. W. Journal of MagneticResonance 2012, 214, 258-262, which is incorporated herein in itsentirety by reference. Fresh batches of parahydrogen were collected in10 L aluminum storage tanks (14745-SHF-GNOS, Holley, Ky., USA), usedwithout Teflon lining or additional modification.

The preparation of PASADENA (see, Bowers, C. R.; Weitekamp, D. P.Physical Review Letters 1986, 57, 2645-2648; and Bowers, C. R.;Weitekamp, D. P. Journal of the American Chemical Society 1987, 109,5541-5542, each of which is incorporated herein in its entirety byreference) precursor molecules was similar to those previously described(see, Waddell, K. W.; Coffey, A. M.; Chekmenev, E. Y. J. Am. Chem. 2011,133, 97-101) with the exception that water was used in place of 99.8%D₂O as a solvent. Briefly, 1,4-bis-(phenyl-3-propane sulfonate)phosphine(0.180 g, 0.32 mmol, Q36333, Isotec, Ohio, USA) was combined with 100 mLH₂O in a 1 L flask. This ambient solution was then degassed with arotary evaporator (model R-215 equipped with V-710 pump, Buchi, NewCastle Del.) fitted with an N₂ (g) input, by decrementing the onboardpressure slowly to avoid boiling, from 70 to 25 mbar over approximately10 minutes. The rhodium catalyst, bis(norbornadiene)rhodium (I)tetrafluoroborate (0.10 g, 0.27 mmol, 45-0230, CAS 36620-11-8, StremChemicals, Mass., USA) was dissolved in 7 mL acetone and was addeddrop-wise to the phosphine ligand solution to limit undesirableprecipitation. After repeating the prior degassing procedure, thiscatalyst solution was mixed with 2-hydroxyethyl acrylate-1-¹³C,2,3,3-d₃(HEA, 97% chemical purity, 99 atom % ¹³C, 98 atom % D (20 mg, 0.16 mmol,Sigma-Aldrich 676071) in a 150 mL square bottle (431430, Corning LifeSciences, N.Y., USA).

Solutions containing unsaturated precursor molecules, catalyst, andligand prepared as described above, were then connected to a previouslydescribed automated parahydrogen polarizer, (see, Waddell, K. W.;Coffey, A. M.; Chekmenev, E. Y. J. Am. Chem. 2011, 133, 97-101 andInternational Patent Application Pub. No. WO 2012/145733, each of whichis incorporated herein in its entirety by reference) equipped with adual-tuned ¹H/¹³C coil. See, Coffey, A. M.; Shchepin, R. V.; Wilkens,K.; Waddell, K. W.; Chekmenev, E. Y. Journal of Magnetic Resonance 2012,220, 94-101, which is incorporated herein in its entirety by reference.Briefly, the chemical reaction was pulse programmed with a commercialNMR console (model KEA, Magritek NZ), to synchronize chemical reactionparameters, decoupling fields, polarization transfer sequences, anddetection of NMR signals. PASADENA precursors were sprayed remotely intoa plastic (polysulfone) reactor located within a 48 mT static magneticfield. The external solution was equilibrated at 65° C. prior tospraying, and 16.5 bar (240 psi) nitrogen gas was used to inject thisheated PASADENA precursor solution into a pressurized atmosphere of 7bar (100 psi) parahydrogen. Immediately following injection, protoncontinuous wave decoupling was applied at a frequency of 2.02 MHz(B₀=47.5 mT) with a magnitude of 5 kHz. This decoupling field wasmaintained for 4 seconds to lock the parahydrogen spin ensemble whilethe hydrogenation reaction went to completion.

The pulse sequences for transferring polarization were appliedimmediately after continuous wave decoupling was turned off (FIG. 2).For the HEP molecule, the t₁, t₂, t₃, and t₄ intervals were 9.75, 50.34,36.20, and 28.28 ms, respectively, calculated by inverting the densitymatrix expressions above (see Theory) assuming a proton-proton couplingof 7.57 Hz, and a carbon-proton scalar coupling asymmetry of 12.86 Hz.See, Goldman, M.; Johannesson, H.; Axelsson, 0.; Karlsson, M. Magn ResonImaging 2005, 23, 153-7, which is incorporated herein in its entirety byreference. The actual couplings could vary somewhat from these valuesdepending on pH and specific attributes of the polarization process suchas temperature and pressure. After polarization transfer, a single freeinduction decay was acquired with 512 points at a receiver bandwidth of5 kHz, for a digital resolution of ˜10 Hz per point.

Described here is a new pulse sequence for prolonging the effectivelifetime of parahydrogen spin order in PHIP experiments performed at lowmagnetic fields in the strong-coupling regime of protons. The sequencetransforms parahydrogen spin order efficiently into heteronuclearmagnetization approximately independent of scalar coupling topology inthree spin moieties (AA′X). This is a ubiquitous moiety in PHIP, beingformed for example in current metabolic imaging agents such as theparahydrogen addition product of fumaric acid (succinate 1-¹³C-2,3-d₂,see, Chekmenev, E. Y.; Hovener, J.; Norton, V. A.; Harris, K.;Batchelder, L. S.; Bhattacharya, P.; Ross, B. D.; Weitekamp, D. P. J AmChem Soc 2008, 130, 4212-3, which is incorporated herein in its entiretyby reference), and more recently in the ester analog (diethyl succinate1-¹³C-2,3-d₂, see, Zacharias, N. M.; Chan, H. R.; Sailasuta, N.; Ross,B. D.; Bhattacharya, P. Journal of the American Chemical Society 2012,134, 934-943, which is incorporated herein in its entirety byreference). This sequence features two asymmetric proton refocusingintervals positioned about a heteronuclear excitation pulse to providefour unique delays (t₁-t₄), which in turn are optimized for thesequential conversion of parahydrogen spin order into heteronuclearmagnetization (FIG. 2). The equations governing evolution of the densityoperator in each interval were described (see Theory) and are linked viaequation numbers to FIG. 2 to provide an overall schematic of spin orderflow from the initial singlet-state to the coupled heteronucleus. Theshorthand hyper-SHIELDED (Singlet to Heteronuclei by Iterative EvolutionLocks Dramatic Enhancement for Delivery) was adopted for quick referencedue to the protective effect on PHIP hyperpolarization.

The analysis of spin dynamics under the influence of hyper-SHIELDEDassumed strongly coupled protons and weak heteronuclear scalar couplings(Eq. 1), with the initial parahydrogen density operator retained withouttruncation and proportional to I₁·I₂ (Eq. 2). Chemical shifts were notconsidered because the effects are small compared to homonuclear protoncouplings at targeted fields in the vicinity of 12 mT or lower, andadditionally because offsets were refocused with 180° pulses on bothchannels placed at ¼ and ¾ of each evolution interval. See, Goldman, M.;Johannesson, H.; Axelsson, O.; Karlsson, M. Magn Reson Imaging 2005, 23,153-7, which is incorporated herein in its entirety by reference.Relative to (truncated) high field density operators proportional toI_(1z)I_(2z), evolution of the low field parahydrogen density operatoris more complex and more efficient in terms of nominal heteronuclearpolarization yield. The time-scale for transferring polarization to aheteronucleus is inversely proportional to the coupling asymmetry andapproaches an asymptote in the limit that the parahydrogen additionproduct becomes symmetric.

The hyper-SHIELDED sequence was applied immediately following a periodof initial proton decoupling, used to maintain equivalence of theparahydrogen protons and thus freeze evolution of the spin densityoperator (see, Goldman, M.; Johannesson, H. Comptes Rendus Physique2005, 6, 575-581, which is incorporated herein in its entirety byreference) until the hydrogenation reaction goes to completion (FIG. 2).After this period of decoupling and chemical addition, the initialdensity matrix evolves from the parahydrogen singlet-state (Eq. 2) tothree terms (Eq. 3a-c, symbols 3a-c in FIG. 2) in the Cartesian productbasis (see, Sorensen, O. W.; Eich, G. W.; Levitt, M. H.; Bodenhausen,G.; Ernst, R. R. Progress in Nuclear Magnetic Resonance Spectroscopy1983, 16, 163-192, which is incorporated herein in its entirety byreference) during the first interval (t₁). A 180° proton x-pulse thenfocuses these three terms of the density matrix into term 4c during theinterval t₂. A 90° y-pulse on the S-nucleus (e.g. carbon-13) then allowsterm 4c to evolve into an additional three terms (symbols 6a-c, FIG. 2)during the interval t₃. Following a proton 180° pulse, these three terms(symbols 6a-c, FIG. 2) collapse into a single term during t₄ (symbol 7b,FIG. 2). This 7b term represents pure S-magnetization (see Eq. 7b), andcan be either rotated to the longitudinal axis for storage with a 90°x-pulse, or left unperturbed in the transverse plane for detection insitu. See, Waddell, K. W.; Coffey, A. M.; Chekmenev, E. Y. J. Am. Chem.2011, 133, 97-101, which is incorporated herein in its entirety byreference. As noted previously, refocusing at the center of theevolution intervals was insufficient to correct for fieldinhomogeneities and therefore nonselective refocusing pulses on bothchannels were interleaved at ¼ and ¾ duration of each evolution intervalto refocus offsets and mitigate the deleterious impact of static fieldinhomogeneities.

A primary advantage of hyper-SHIELDED is that polarization yield isobtained approximately independent of coupling topology (FIG. 3), andthis nearly uniform response of polarization is obtained withoutpiecewise construction or recursive application of the sequence. See,Goldman, M.; Johannesson, H.; Axelsson, O.; Karlsson, M. Magn ResonImaging 2005, 23, 153-7, which is incorporated herein in its entirety byreference. The difficulty of attaining uniform transfer efficiency inthe conversion of parahydrogen spin order into heteronuclearmagnetization can be appreciated qualitatively by comparison to familiarpolarization transfer sequences such as INEPT (see, Morris, G. A.;Freeman, R. Journal of the American Chemical Society 1979, 101, 760-762,which is incorporated herein in its entirety by reference) or HMQC (see,Muller, L. Journal of the American Chemical Society 1979, 101,4481-4484, which is incorporated herein in its entirety by reference).In conventional sequences, transverse magnetization in coupled AA′X spinsystems evolve towards antiphase terms regardless of coupling asymmetry.By contrast, the parahydrogen singlet state formed with PASADENA becomesstationary in the limit that AA′X collapses to A₂X, as seen from Eq. 3by substituting Δ=0 (giving cos(θ)=0 and sin(θ)=1). For additionaldetail on the theoretical aspects of PHIP, we refer readers to recentreviews by Green and coworkers (Green, R. A.; Adams, R. W.; Duckett, S.B.; Mewis, R. E.; Williamson, D. C.; Green, G. G. R. Progress in NuclearMagnetic Resonance Spectroscopy 2012, which is incorporated herein inits entirety by reference) and Natterer et al. (Natterer, J.; Bargon, J.Progress in Nuclear Magnetic Resonance Spectroscopy 1997, 31, 293-315,which is incorporated herein in its entirety by reference).

The nominal sensitivity of hyper-SHIELDED transfer efficiency was mappedto scalar coupling topology across a range of conceivable PASADENAaddition products. For each unique set of couplings (J₁₂,|J_(1S)−J_(2S)|), the density matrix equations (see Theory) wereinverted to solve for the optimal set of evolution intervals. Couplingasymmetry (|J_(1S)−J_(2S)|) and homonuclear proton couplings (J₁₂) werevaried from 0 Hz to 45 Hz and 0 Hz to 10 Hz, respectively, against atotal pulse sequence duration constraint of 300 ms (FIG. 3). Asillustrated in FIG. 3, the transition from zero to uniformly efficienttransfer with hyper-SHIELDED is steep. Heteronuclear polarizationsaturates on a broad plateau of uniform efficiency with as little as 8Hz coupling asymmetry. Then as coupling asymmetry increases toward 35Hz, homonuclear proton couplings must increase to maintain uniformefficiency.

This saturation plateau would expand if the total pulse sequenceduration constraint was increased from 300 ms if application warranted,although the sequence was designed in particular to improve efficiencyin the low asymmetry regime and therefore improve polarization yield innitrogen-15 labeled PHIP addition products such as ethylamine,diethylamine, and choline which are known to have small asymmetries. Inother words, without wishing to be bound by any particular theory, thetotal pulse sequence duration constraint of 300 ms causes less thanmaximum magnetization transfer with certain J-coupling asymmetries, butwere the constraint removed, the magnetization transfer could bemaximized given sufficient pulse duration.

Example 2 Experimental Verification of Hyper-SHIELDED Pulse Sequence andComparative Pulse Sequence

To highlight the performance of hyper-SHIELDED in nearly symmetric PHIPproducts, optimal efficiency was compared experimentally to a widelyused transfer sequence (hereinafter, “GPS”) previously reported byGoldman and coworkers (see, Goldman, M.; Johannesson, H.; Axelsson, O.;Karlsson, M. Magn Reson Imaging 2005, 23, 153-7, which is incorporatedherein in its entirety by reference). GPS provided a convenient testpoint given that it was already implemented in a non-recursive versionon our pulse programmable polarizer. See, Waddell, K. W.; Coffey, A. M.;Chekmenev, E. Y. J. Am. Chem. 2011, 133, 97-101, which is incorporatedherein in its entirety by reference. Although not yet experimentallydemonstrated, it is noted that a series of three piecewise optimalsolutions were recently reported by Kadlecek and coworkers. See,Kadlecek, S.; Emami, K.; Ishii, M.; Rizi, R. J Magn Reson 2011, 205,9-13, which is incorporated herein in its entirety by reference. Thisset of sequences may offer solutions to the transfer problem in threedistinct coupling asymmetry epochs, but utilizes a different pulsesequence for each epoch. In other words, the pulse sequence cannot beadapted to transfer nuclear singlet state spin order into heteronuclearmagnetization localized on S at any |J_(1S)−J_(2S)| when the independentevolution intervals are optimized. A possible disadvantage of thissequences reported by Kadlecek and coworkers is that the scalarcouplings present in the reactor are not often known precisely at thereaction conditions, and can differ significantly from separatedetermination from high resolution NMR results obtained at nearlyequivalent pH. In other words, if the scalar couplings present in thereactor differ from separate determination from high resolution NMRresults, then optimizing magnetization transfer could require the use ofa different pulse sequence from a different coupling asymmetry epoch. Itis often necessary to empirically optimize transfer sequences to obtainbest results, and this is made easier with evolution intervals that canbe adjusted along a continuum within a consolidated sequence such ashyper-SHIELDED.

For comparison with the experimentally validated GPS sequence, densitymatrix equations for both sequences were inverted to find the optimalevolution intervals that maximize polarization yield as a function ofcoupling asymmetry at a common proton coupling (J₁₂) of 7.5 Hz. Asillustrated in FIG. 3, the dependence of polarization yield in the smallasymmetry regime is relatively insensitive to J₁₂. We found thatpolarization yields reach uniform efficiency more rapidly as a functionof asymmetry in hyper-SHIELDED versus the non-recursive application ofGPS (see, Goldman, M.; Johannesson, H. Comptes Rendus Physique 2005, 6,575-581, which is incorporated herein in its entirety by reference), andhigh levels of polarization are sustained across a broad range ofasymmetries (FIG. 4). For the PASADENA product, 2-hydroxy,1-¹³C-ethylpropionate-d₃, hyper-SHIELDED was predicted to be equivalentto GPS, and this was verified experimentally (FIGS. 5-7), where a factorof 5,000,000 enhancement was obtained at a static field of 48 mT.Hyper-SHIELDED is predicted to give approximately 18 percent higherpolarization yield for the biologically important class of nitrogen-15labeled PASADENA products such as ethylamine, diethylamine, and choline.The use of four independent evolution intervals enables fast saturationof polarization as a function of spin-system asymmetry, and providesnearly uniform efficiency over a broad range in a consolidated sequencewithout requiring recursive application, hence providing a streamlinedand broadly efficient transfer sequence.

The text that follows is the hyper-SHIELDED minimization code:

function tau = Pump(J) % Calculating the time delays for hS3 % t = arrayof time delays (4 delays) % J(1) = proton-proton coupling % J(2) andJ(3) = proton-carbon couplings delta = (J(2)−J(3))/(2*J(1)); theta =asin(1/(sqrt(1+delta{circumflex over ( )}2))); omega =J(1)*(sqrt(1+delta{circumflex over ( )}2));  for k=1:1000; t1=0.0001*k;for l=1:1000;  t2=0.0001*1;  F(k,l) =abs(−0.5*sin(2*theta)*(cos(2*theta)... +2*((sin(theta)){circumflex over( )}2)*cos(2*pi*omega*t2)... −2*((cos(theta)){circumflex over( )}2)*cos(2*pi*omega*t1)...+cos(2*theta)*cos(2*pi*omega*t1)*cos(2*pi*omega*t2)...+sin(2*pi*omega*t1)*sin(2*pi*omega*t2))); end  end  [K,L] =find(F>(max(F(:))−0.0001));  len=length(K);  for n=1:len;Dur(n)=K(n)+L(n);  end  [minDur,N]=find(Dur==min(Dur)); tau(1)=K(min(N))*0.0001;  tau(2)=L(min(N))*0.0001; P(1)=F(K(min(N)),L(min(N)));  for k=1:1000; t3=0.0001*k; for l=1:1000; t4=0.0001*1;  F(k,l) = abs(cos(theta)*cos(2*pi*omega*t3)*sin(2*pi*omega*t4)...−sin(theta)*sin(2*theta)*sin(2*pi*omega*t3)...−cos(theta)*cos(2*theta)*sin(2*pi*omega*t3)... *cos(2*pi*omega*t4)); end end  [K,L] = find(F>(max(F(:))−0.0001));  len=length(K);  for n=1:len;Dur(n)=K(n)+L(n);  end  [minDur,N]=find(Dur==min(Dur)); tau(3)=K(min(N))*0.0001;  tau(4)=L(min(N))*0.0001; P(2)=F(K(min(N)),L(min(N)));  t1=tau(1);  t2=tau(2);  t3=tau(3); t4=tau(4);  tau(5)=P(1)*P(2); tau(6)=abs((sin(theta)*sin(2*theta)*sin(2*pi*omega*t2)...+cos(theta)*cos(2*theta)*cos(2*pi*omega*t1)*sin(2*pi*omega*t2)...−cos(theta)*sin(2*pi*omega*t1)*cos(2*pi*omega*t2))...*(0.25*sin(4*theta)...+0.25*sin(4*theta)*cos(2*pi*omega*t3)*cos(2*pi*omega*t4)...+sin(2*theta)*(((sin(theta)){circumflex over( )}2)*cos(2*pi*omega*t3)... −((cos(theta)){circumflex over( )}2)*cos(2*pi*omega*t4))...+cos(theta)*sin(theta)*sin(2*pi*omega*t3)*sin(2*pi*omega*t4))...−0.5*sin(2*theta)*(cos(2*theta)... +2*((sin(theta)){circumflex over( )}2)*cos(2*pi*omega*t2)... −2*((cos(theta)){circumflex over( )}2)*cos(2*pi*omega*t1)...+cos(2*theta)*cos(2*pi*omega*t1)*cos(2*pi*omega*t2)...+sin(2*pi*omega*t1)*sin(2*pi*omega*t2))...*(cos(theta)*cos(2*pi*omega*t3)*sin(2*pi*omega*t4)...−sin(theta)*sin(2*theta)*sin(2*pi*omega*t3)...−cos(theta)*cos(2*theta)*sin(2*pi*omega*t3)*cos(2*pi*omega*t4))); end

What is claimed is:
 1. A method of performing Nuclear Magnetic Resonance(NMR) spectroscopy or Magnetic Resonance Imaging (MRI), the methodcomprising: a) generating a compound comprising a first nuclear species(I₁), a second nuclear species (I₂), a third nuclear species (S), aheteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) and a nuclear singletstate spin order localized on I₁ and I₂; b) transferring the nuclearsinglet state spin order into heteronuclear magnetization localized on Sby applying a single, non-recursive pulse sequence at a low magneticfield in the strong coupling regime of protons; and c) performing NMRspectroscopy or MRI with the compound comprising heteronuclearmagnetization localized on S, wherein |J_(1S)−J_(2S)| is non-zero,wherein the pulse sequence comprises a plurality of sequential radiofrequency pulses separated by independent evolution intervals, whereinthe pulse sequence transfers at least about 75% of the nuclear singletstate spin order into heteronuclear magnetization localized on S at any|J_(1S)−J_(2S)| when the independent evolution intervals are optimized,and wherein the pulse sequence comprises the following sequential steps:a) waiting a time t₁ after generating the compound; b) applying a180(+x) pulse on I₁ and I₂; c) waiting a time t₂; d) applying a 90(+y)pulse on S; e) waiting a time t₃; f) applying a 180(+x) pulse on I₁ andI₂; g) waiting a time t₄; and h) applying a 90(+x) pulse on S.
 2. Themethod of claim 1, wherein generating a compound compriseshyperpolarizing the compound by parahydrogen induced polarization(PHIP).
 3. The method of claim 1, wherein the compound has a HamiltonianofH=2π[J ₁₂(I ₁ ·I ₂)+J _(1S) I _(1z) S _(z) +J _(2S) I _(2z) S _(z)]. 4.The method of claim 1, wherein the pulse sequence comprises a firstportion and a second portion, wherein the first portion converts thenuclear singlet state spin order localized on I₁ and I₂ into a purestate which is coupled to S, and wherein the second portion converts thepure state which is coupled to S into longitudinal net magnetization onS.
 5. The method of claim 1, wherein t₁, t₂, t₃ and t₄ are selected tomaximize transfer of the nuclear singlet state spin order localized onI₁ and I₂ into longitudinal net magnetization on S.
 6. The method of Themethod of claim 1, wherein t₁ and t₂ are selected to maximize transferof the nuclear singlet state spin order localized on I₁ and I₂ into apure state which is coupled to S, and wherein t₃ and t₄ are selected tomaximize transfer of the pure state which is coupled to S intolongitudinal net magnetization on S.
 7. The method of claim 1, whereinthe pulse sequence transfers at least about 90% of the nuclear singletstate spin order into heteronuclear magnetization localized on S at any|J_(1S)−J_(2S)| when the independent evolution intervals are optimized.8. An NMR spectroscopy or MRI system configured to perform the method ofclaim
 1. 9. A method of performing Nuclear Magnetic Resonance (NMR)spectroscopy or Magnetic Resonance Imaging (MRI), the method comprising:a) generating a compound comprising a first nuclear species (I₁), asecond nuclear species (I₂), a third nuclear species (S), aheteronuclear coupling asymmetry (|J_(1S)−J_(2S)|) and nuclear singletstate spin order localized on I₁ and I₂; b) transferring the nuclearsinglet state spin order into heteronuclear magnetization localized on Sby applying a single, non-recursive pulse sequence at a low magneticfield in the strong coupling regime of protons; and c) performing NMRspectroscopy or MRI with the compound comprising heteronuclearmagnetization localized on S, wherein |J_(1S)−J_(2S)| is non-zero,wherein the pulse sequence comprises a plurality of sequential radiofrequency pulses separated by independent evolution intervals, whereinthe pulse sequence transfers at least about 75% of the nuclear singletstate spin order into heteronuclear magnetization localized on S at an|J_(1S)−J_(2S)| when the independent evolution intervals are optimized,and wherein the hyperpolarized sample further comprises a fourth nuclearspecies (R), and wherein the pulse sequence comprises the followingsequential steps: a) waiting a time t₁ after generating the compound; b)applying a 180(+x) pulse on S; c) waiting a time t₂; d) applying a180(+x) pulse on I₁ and I₂; e) waiting a time t₃; f) applying a 90(+y)pulse on S; g) waiting a time t₄; h) applying a 180(+x) pulse on S; i)waiting a time t₅; j) applying a 180(+x) pulse on I₁ and I₂; k) waitinga time t₆; and l) applying a 90(+x) pulse on S.
 10. The method of claim9, wherein t₁, t₂, t₃, t₄, t₅ and t₆ are selected to maximize transferof the nuclear singlet state spin order localized on I₁ and I₂ intolongitudinal net magnetization on S.
 11. The method of claim 9, whereint₁, t₂ and t₃ are selected to maximize transfer of the nuclear singletstate spin order localized on I₁ and I₂ into a pure state which iscoupled to S, and wherein t₄, t₅ and t₆ are selected to maximizetransfer of the pure state which is coupled to S into longitudinal netmagnetization on S.
 12. A method of performing Nuclear MagneticResonance (NMR) spectroscopy or Magnetic Resonance Imaging (MRI), themethod comprising: a) generating a compound comprising a first nuclearspecies (I₁), a second nuclear species (I₂), a third nuclear species(S), a fourth nuclear species (R) and a nuclear singlet state spin orderlocalized on I₁ and I₂; b) transferring the nuclear singlet state spinorder into heteronuclear magnetization localized on S by applying apulse sequence at a low magnetic field in the strong coupling regime ofprotons; and c) performing NMR spectroscopy or MRI with the compoundcomprising heteronuclear magnetization localized on S; wherein the pulsesequence comprises the following sequential steps: a) waiting a time t₁after hyperpolarizing the sample; b) applying a 180(+x) pulse on S; c)waiting a time t₂; d) applying a 180(+x) pulse on I₁ and I₂; e) waitinga time t₃; f) applying a 90(+y) pulse on S; g) waiting a time t₄; h)applying a 180(+x) pulse on S; i) waiting a time t₅; j) applying a180(+x) pulse on I₁ and I₂; k) waiting a time t₆; and l) applying a90(+x) pulse on S.
 13. The method of claim 12, wherein the compound hasa Hamiltonian ofH=2π[J ₁₂(I _(1x) I _(2x) +I _(1y) I _(2y) +I _(1z) I _(2z))+J _(1S) I_(1z) S _(z) +J _(1R) I _(1z) R _(z) +J _(2S) I _(2z) S _(z) +J _(2R) I_(2z) R _(z) +J _(SR) S _(z) R _(z)].
 14. The method of claim 12,wherein t₁, t₂, t₃, t₄, t₅ and t₆ are selected to maximize transfer ofthe nuclear singlet state spin order localized on I₁ and I₂ intolongitudinal net magnetization on S.
 15. The method of claim 12, whereint₁, t₂ and t₃ are selected to maximize transfer of the nuclear singletstate spin order localized on I₁ and I₂ into a pure state which iscoupled to S, and wherein t₄, t₅ and t₆ are selected to maximizetransfer of the pure state which is coupled to S into longitudinal netmagnetization on S.
 16. A method of performing Nuclear MagneticResonance (NMR) spectroscopy or Magnetic Resonance Imaging (MRI), themethod comprising: a) determining J-couplings for a compound comprisinga first nuclear species (I₁), a second nuclear species (I₂), a thirdnuclear species (S), a heteronuclear coupling asymmetry(|J_(1S)−J_(2S)|) and a nuclear singlet state spin order localized on I₁and I₂; b) calculating optimal evolution intervals for a single,non-recursive pulse sequence at low magnetic field in the strongcoupling regime of protons using the J-couplings, the pulse sequencecomprising a sequential plurality of radio frequency pulses separated byindependent evolution intervals; c) generating the compound; d)transferring the nuclear singlet state spin order into heteronuclearmagnetization localized on S by applying the pulse sequence with optimalevolution intervals to the compound; and e) performing NMR spectroscopyor MRI with the compound comprising heteronuclear magnetizationlocalized on S, wherein |J_(1S)−J_(2S)| is non-zero, wherein the pulsesequence transfers at least about 75% of the nuclear singlet state spinorder into heteronuclear magnetization localized on S at any|J_(1S)−J_(2S)|, and wherein calculating optimal evolution intervalscomprises inverting a density matrix expression representing theevolution of spin states of the compound during application of the pulsesequence to the compound, minimizing the difference between a densitymatrix expression representing the evolution of spin states of thecompound during application of the pulse sequence and a desired statewhich is coupled to S, or a combination thereof.
 17. The method of claim16, wherein determining J-couplings for a compound comprisesexperimentally determining J-couplings, theoretically calculatingJ-couplings and combinations thereof.